1. The Field of the Invention.
The present invention relates generally to a method and apparatus for teaching or representing the relationship of the trigonometric functions between the unit circle and the Cartesian or rectangular coordinate system. More particularly, the present invention relates to a method or apparatus in which the trigonometric functions are physically represented and transformed between a unit circle configuration and a rectangular coordinate system configuration.
2. The Background Art.
Teaching is most often performed by a teacher lecturing a group of students on a given subject. While some students have the desire, self discipline, focus, attention and maturity to learn, other students may face challenges to learning. Typically, the teacher is faced with the challenge of grasping the students' attention and causing them to think. It is generally considered that the learning and teaching process is facilitated by visualization, or the ability of the teacher to show and demonstrate what is being taught, and the ability of the student to perceive. Furthermore, it is generally considered that the learning process is facilitated by hands-on experience. Students seem more interested in, and better able to understand, matters which they can visualize and touch. Therefore, there is a continuing desire to develop new visual aids and hands-on experiences to aid in teaching.
For example, trigonometric functions involve the ratios between the sides of a right triangle 900 having legs 904 and 908 and a hypotenuse 912, as shown in FIG. 21. The ratios only depend on the size of the angle .theta.. A unit circle 920 is often used to visually describe or represent the various trigonometric functions. The unit circle 920 has a center point 924, or origin, and a radius of one, or the hypotenuse 912 of length one. Various lines represent the trigonometric functions and are oriented with respect to the unit circle 920 based on the particular trigonometric function.
In addition, the trigonometric functions are periodic functions which may be defined in the Cartesian or rectangular coordinate system. Although the trigonometric functions are usually taught with respect to both the unit circle and rectangular coordinate system, the relationship between the unit circle and rectangular coordinate system is rarely, if ever, pointed out. Text books may even proceed directly from the representation of the trigonometric functions in the unit circle, to a representation in the rectangular coordinate system, without the slightest indication that the two systems may relate, or how. Therefore, it would be desirable to teach this relationship between the two systems in order to further the understanding of the trigonometric functions.
Therefore, it would be advantageous to develop a method and apparatus to teach the relationship of the trigonometric functions between the unit circle and the rectangular coordinate system. It would also be advantageous to develop such a method and apparatus capable of visually demonstrating the relationship. It would also be advantageous to develop such a method and apparatus that would allow hands-on experimentation.